Method, device, computer program and computer program product for determining a representation of a signal

Abstract

A method for determining a representation (y) of a signal (s) comprise selecting a predetermined number (m) of row vectors (v 1 , . . . , vm) from a predetermined measurement matrix (M). The predetermined measurement matrix (M) is predetermined dependent on a product of a predetermined Hadamard matrix or generalized Hadamard matrix (H) and a predetermined representation matrix(B). The predetermined representation matrix (B) represents a predetermined basis for the signal(s). The method further comprises determining a respective inner product of the signal (s) and each of the predetermined number (m) of selected row vectors (v 1 , . . . , vm) resulting in a predetermined number (m) of measurements (y 1 , . . . , ym) forming the representation (y) of the signal (s).

We claim: 
     
       1. A method for determining a representation (y) of a signal (s), comprising:
 selecting, with a processing unit, a predetermined number (m) of row vectors (v 1 , . . . , vm) from a predetermined measurement matrix (M), the predetermined measurement matrix (M) being predetermined dependent on a product of a predetermined Hadamard matrix or generalized Hadamard matrix (H) and a predetermined representation matrix (B), the predetermined representation matrix (B) representing a predetermined basis for the signal (s); and 
 determining, with the processing unit, a respective inner product of the signal (s) and each of the predetermined number (m) of selected row vectors (v 1 , . . . , vm) resulting in a predetermined number (m) of measurements (y 1 , . . . , ym) forming the representation (y) of the signal (s). 
 
     
     
       2. The method according to  claim 1 , wherein a Fourier matrix is used as the generalized Hadamard matrix (H). 
     
     
       3. The method according to  claim 1 , wherein the selection of the predetermined number (m) of the row vectors (v 1 , . . . , vm) comprises selecting the predetermined number (m) of the row vectors (v 1 , . . . , vm) uniformly at random from all row vectors (vi) of the predetermined measurement matrix (M). 
     
     
       4. The method according to  claim 1 , wherein the predetermined representation matrix (B) or predetermined basis for the signal (s) is being selected such that the signal (s) is k-sparse or with respect to a predetermined threshold approximately k-sparse under the predetermined basis for the signal (s) with a sparsity (k) being smaller than a length (n) of the signal (s). 
     
     
       5. A non-transitory computer readable storage medium tangibly embodying a computer readable program code having computer readable instructions which when implemented, cause a computer to carry out the steps of the method according to  claim 1 . 
     
     
       6. A method for determining a representation (y) of a signal (s), comprising:
 determining, with a processing unit, a first transform (b) dependent on the signal (s) by multiplying a predetermined representation matrix (B) representing a predetermined basis for the signal (s) with the signal (s) or by applying a first transform algorithm (transf(s,B)) based on the predetermined basis for the signal (s) to the signal (s); 
 determining, with the processing unit, a second transform (h) dependent on the first transform (b) by multiplying a predetermined Hadamard matrix or generalized Hadamard matrix (H) with the first transform (b) or by applying as a second transform algorithm (transf(b,H)) a Hadamard transform or fast Hadamard transform to the first transform (b); and 
 selecting, with the processing unit, a predetermined number (m) of measurements (y 1 , . . . , ym) forming the representation (y) of the signal (s) from the second transform (h). 
 
     
     
       7. The method according to  claim 6 , wherein a Fourier matrix is used as the generalized Hadamard matrix (H). 
     
     
       8. The method according to  claim 6 , wherein the selection of the measurements (y 1 , . . . , ym) comprises selecting the measurements (y 1 , . . . , ym), from all elements of the second transform (h). 
     
     
       9. The method according to  claim 6 , wherein the predetermined representation matrix (B) or predetermined basis for the signal (s) is being selected such that the signal (s) is k-sparse or with respect to a predetermined threshold approximately k-sparse under the predetermined basis for the signal (s) with a sparsity (k) being smaller than a length (n) of the signal (s). 
     
     
       10. A non-transitory computer readable storage medium tangibly embodying a computer readable program code having computer readable instructions which when implemented, cause a computer to carry out the steps of the method according to  claim 6 . 
     
     
       11. A device for determining a representation (y) of a signal (s) comprising:
 at least one processing unit (CPU); 
 at least one memory unit (MEM); 
 at least one signal source (SRC) being coupled to said at least one CPU; and 
 at least one signal processing unit (SPU); 
 wherein said at least one CPU or at least one SPU (i) selects a predetermined number (m) of row vectors (v 1 , . . . , vm) from a predetermined measurement matrix (M), the predetermined measurement matrix (M) being predetermined dependent on a product of a predetermined Hadamard matrix or generalized Hadamard matrix (H) and a predetermined representation matrix (B), the predetermined representation matrix (B) representing a predetermined basis for the signal (s), and (ii) determines a respective inner product of the signal (s) and each of the predetermined number (m) of selected row vectors (v 1 , . . . , vm) resulting in a predetermined number (m) of measurements (yl, . . . , ym) forming the representation (y) of the signal (s). 
 
     
     
       12. The device according to  claim 11 , wherein the CPU and SPU operate simultaneously. 
     
     
       13. The device according to  claim 11 , wherein the CPU and SPU operate sequentially with respect to each other. 
     
     
       14. The device according to  claim 11 , further comprising at least one input/output unit. 
     
     
       15. A device for determining a representation (y) of a signal (s) comprising:
 at least one processing unit (CPU); 
 at least one memory unit (MEM); 
 at least one signal source (SRC) being coupled to said at least one CPU; and 
 at least one signal processing unit (SPU); 
 wherein said at least one CPU or at least one SPU (i) determines a first transform (b) dependent on the signal (s) by multiplying a predetermined representation matrix (B) representing a predetermined basis for the signal (s) with the signal (s) or by applying a first transform algorithm (transf(s,B)) based on the predetermined basis for the signal (s) to the signal (s), (ii) determines a second transform (h) dependent on the first transform (b) by multiplying a predetermined Hadamard matrix or generalized Hadamard matrix (H) with the first transform (b) or by applying as a second transform algorithm (transf(b,H)) a Hadamard transform or fast Hadamard transform to the first transform (b) and (iii) selects a predetermined number (m) of measurements (yl, . . . , ym) forming the representation (y) of the signal (s) from the second transform (h). 
 
     
     
       16. The device according to  claim 15 , wherein the CPU and SPU operate simultaneously. 
     
     
       17. The device according to  claim 15 , wherein the CPU and SPU operate sequentially with respect to each other. 
     
     
       18. The device according to  claim 15 , further comprising at least one input/output unit.